Can you solve for x and y in this complex numbers equation?

In summary, to find the values of x and y for the given equation (x+y)+i(x-y)=14.8+6.2i, you need to set up a system of equations where the real parts and imaginary parts of the complex numbers are equal. Solving this system will give you the values of x and y.
  • #1
cowboi12345
7
0
I have to find x and y for:

(x+y)+i(x-y)=14.8+6.2i


how to do?
 
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  • #2
In order for two complex numbers z and w to be equal, Re(z)=Re(w) and Im(z)=Im(w). In this case, you get the system of equations x+y=14.8 and x-y=6.2, which is a system you can solve.
 
  • #3
Char. Limit said:
In order for two complex numbers z and w to be equal, Re(z)=Re(w) and Im(z)=Im(w). In this case, you get the system of equations x+y=14.8 and x-y=6.2, which is a system you can solve.

OHHHH!...THANKS ALOT! :smile:
 

What are complex numbers?

Complex numbers are numbers that consist of a real part and an imaginary part, denoted by a + bi, where a is the real part and bi is the imaginary part with i representing the square root of -1.

How do you add and subtract complex numbers?

To add or subtract complex numbers, you simply add or subtract the real parts and the imaginary parts separately. For example, (3 + 4i) + (5 + 2i) = (3+5) + (4i+2i) = 8 + 6i. Same goes for subtraction, (3 + 4i) - (5 + 2i) = (3-5) + (4i-2i) = -2 + 2i.

How do you multiply complex numbers?

To multiply complex numbers, you use the FOIL method (First, Outer, Inner, Last). For example, (3 + 4i)(5 + 2i) = 3(5) + 3(2i) + 4i(5) + 4i(2i) = 15 + 6i + 20i + 8i^2 = 15 + 26i - 8 = 7 + 26i. Remember that i^2 = -1.

How do you divide complex numbers?

To divide complex numbers, you multiply the numerator and denominator by the complex conjugate of the denominator. The complex conjugate of a + bi is a - bi. For example, (3 + 4i) / (5 + 2i) = (3 + 4i)(5 - 2i) / (5 + 2i)(5 - 2i) = (15 - 6i + 20i - 8i^2) / (25 - 4i^2) = (23 + 14i) / 29 = 23/29 + (14/29)i.

What are some real-world applications of complex numbers?

Complex numbers have many real-world applications, such as in electrical engineering, signal processing, and quantum mechanics. They are also used to represent and solve problems in fluid dynamics, control systems, and circuit analysis. Additionally, complex numbers are used in computer graphics and game development to represent 2D and 3D space.

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